Winds toppled trees and branches across the state Sunday, blocking roads and causing scattered power outages.

The National Weather Service had predicted gusts of wind at up to 45 miles per hour in the Boston area, and issued a wind advisory for the whole state.

And the trees and branches fell, knocking out power to homes and businesses from Methuen to Norfolk.

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“This is typical of what we would expect in high winds. You have trees moving and wires moving and they come into contact with one another and take out the wires,” NStar spokesman Bill Zamparelli said.

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A tree fell on a power line in Topsfield, knocking out electricity to about 4,500 customers in Topsfield and Boxford, a National Grid spokesman said.

“It’s pretty windy out there, so wind may have been a factor,” said spokesman David Graves.

High winds also felled three sections of power line in Acton and Sudbury Sunday morning, leaving customers without electricity, he said.

In Winchester, about 400 people were without power, some because of what appeared to be a fallen branch and others because of an outage near Winchester Center, Zamparelli said. Because wires near Winchester’s downtown area are both above and below ground, crews were still trying to find the problem Sunday afternoon, Zamparelli said.

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More outages were reported late Sunday afternoon, with 5,700 NStar customers without power across the state, Zamparelli said.

Power lines and a few poles were down in Burlington, Framingham, Sudbury, and Weston, with scattered outages in surrounding towns.

“We’re going to see this all day long because of the high winds, it’s just part of what we do,” Zamparelli said Sunday afternoon. “It’s usually high winds that cause the problems, it’s not so much snow or rain.”

By 9:15 p.m. Sunday, power was restored to all but 1,600 NStar customers in Massachusetts, the company said.

In northern New England, the winds caused even more trouble. The Associated Press reported that more than 23,800 customers of Central Maine Power were without power, along with about 13,800 Public Service Company of New Hampshire customers and another 5,400 served by the New Hampshire Electric Cooperative. Green Mountain Power in Vermont reported more than 4,000 outages.

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In Laconia, N.H., strong winds knocked down a tree that struck and killed a 54-year-old Tilton man Sunday, according to police. The man was working on clearing a fallen tree from a Davidson Drive property about 4 p.m. when the other tree struck him, police said in a statement. His identity was being withheld Sunday night pending notification of his family.

After the blustery end to the weekend, National Weather Service meteorologist Alan Dunham said Monday should be clear and remain cold, with sunny skies and highs not getting out of the 30s. Winds will probably slow too, according to the National Weather Service, with gusts reaching just around 24 miles per hour.

Clouds could come in on Tuesday, with rain possible and highs rising to the mid-40s.

Wednesday is expected to be rainy but warmer, with highs near 50 degrees in Boston. Some areas in Southern New Hampshire and Western Massachusetts may get a mix of rain and snow, Dunham said.

“It’s not going to be a great travel day, weather-wise, but it’ll be mostly rain,” he said.

Globe correspondent Jaclyn Reiss contributed to this report. Gal Tziperman Lotan can be reached at gal.lotan@globe.com.